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arXiv · 2607.11763

Local-global compatibility of automorphic Galois representations over CM fields at $p$

Lambert A'Campo·Bence Hevesi·Jack A. Thorne·Dmitri Whitmore
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Abstract

Let $F$ be a CM number field; then, to any cuspidal, regular algebraic automorphic representation of $\mathrm{GL}_n(\mathbf{A}_F)$ is associated a compatible system of $p$-adic Galois representations of the absolute Galois group of $F$. We prove that these representations are potentially semi-stable, in the sense of $p$-adic Hodge theory, and satisfy compatibility with the local Langlands correspondence, up to semi-simplification.

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Lambert A'Campo, Bence Hevesi, Jack A. Thorne, Dmitri Whitmore. 2026-07-13. Local-global compatibility of automorphic Galois representations over CM fields at $p$. https://arxiv.org/abs/2607.11763

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